量子关联在Cop and Robber博弈中的作用
The role of quantum correlations in Cop and Robber game
摘要：
我们介绍和研究量化版本的警察和强盗的游戏。我们通过使用图保持量子操作来实现这一点，图保持量子操作是保持图的随机操作的量子模拟。我们提供了达到给定状态所需的操作数量的紧界。通过将它们扩展到受控操作，我们定义了一个量子控制的Cop and Robber博弈，它扩展了经典的Cop and Robber博弈，以及经典控制的量子Cop and Robber博弈。与引入量子博弈的典型方案相比，我们假设双方都可以利用对手策略的全部信息。我们表明，利用对手的状态的充分知识不提供优势。此外，对于经典的cop-win图，捕获Robber的机会也在减少。这个结果并不取决于所选择的进化模型。另一方面，执行受控量子操作的可能性允许在几乎所有经典的cop-win图上捕获Robber。通过这一点，我们证明，它是必要的，以丰富的结构之间的相关性的球员的系统，以提供一个非平凡的量化警察和强盗的游戏。因此，量子控制的操作提供了一个显着的优势，超过经典控制的量子操作。
英文摘要：
We introduce and study quantized versions of Cop and Robber game. We achieve this by using graph-preserving quantum operations, which are the quantum analogues of stochastic operations preserving the graph. We provide the tight bound for the number of operations required to reach the given state. By extending them to the controlled operations, we define a quantum-controlled Cop and Robber game, which expands the classical Cop and Robber game, as well as the classically controlled quantum Cop and Robber game. In contrast to the typical scheme for introducing quantum games, we assume that both parties can utilise full information about the opponent's strategy. We show that the utilisation of the full knowledge about the opponent's state does not provide the advantage. Moreover, the chances of catching the Robber decrease for classical cop-win graphs. This result does not depend on the chosen model of evolution. On the other hand, the possibility to execute controlled quantum operations allows catching the Robber on almost all classical cop-win graphs. By this, we demonstrate that it is necessary to enrich the structure of correlations between the players' systems to provide a non-trivial quantized Cop and Robber game. Thus the quantum controlled operations offer a significant advantage over the classically controlled quantum operations.
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